Algorithm for optimal ICD configuration using a coupled wellbore-reservoir model

ABSTRACT

The disclosed embodiments include a method, apparatus, and computer program product for improving production of an oil well. For example, one disclosed embodiment includes a system that includes at least one processor and at least one memory coupled to the at least one processor and storing instructions that when executed by the at least one processor performs operations for generating a model of a wellbore in a wellbore simulator. The at least one processor further executes an algorithm that determines optimal parameters for inflow control devices (ICD) along a horizontal portion of the wellbore. The determined optimal parameters of the inflow control devices would yield a substantially uniform approach of at least one of water and gas along the horizontal portion of the wellbore.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a U.S. National Stage patent application ofInternational Patent Application No. PCT/US2013/053263, filed on Aug. 1,2013, the benefit of which is claimed and the disclosure of which isincorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION Field of the Invention

The present disclosure relates generally to the recovery of subterraneandeposits and more specifically to methods and systems for improvingproduction of an oil well by optimizing inflow control device parametersalong a horizontal wellbore using an algorithm.

Discussion of the Related Art

Horizontal wellbores, as opposed to vertical wells, are often favored byoperators for exploiting narrow, oil-bearing formations to maximizecontact with the pay zone. However, as depicted in FIG. 1, these wellsare subject to early water and gas coning toward the heel because of theflow's frictional pressure drops along the horizontal section. Moreover,variations in permeability can result in unbalanced inflow along thehorizontal section and accelerate early water and gas breakthrough anduneven inflow downhole. These conditions can limit sweep efficiency andreduce hydrocarbon recovery from horizontal wells, leaving bypassed oil.

To combat the above problem, inflow control devices (ICDs) are used toincrease performance of horizontal wells in unfavorable environments.ICDs are designed to improve completion performance and efficiency bybalancing inflow throughout the length of a completion. By using ICDs,it is possible to create a homogeneous production profile that caneffectively delay the water/gas breakthrough while increasing oilrecovery as a consequence.

BRIEF DESCRIPTION OF THE DRAWINGS

Illustrative embodiments of the present invention are described indetail below with reference to the attached drawing figures, which areincorporated by reference herein and wherein:

FIG. 1 is a diagram illustrating an example of a horizontal well withoutthe use of inflow control devices in accordance with the disclosedembodiments;

FIG. 2 is a diagram illustrating an example of a horizontal well thatuses inflow control devices in accordance with the disclosedembodiments;

FIG. 3 is a graph that compares oil production versus water cut for ahorizontal well that uses inflow control devices and a horizontal wellthat does not use inflow control devices in accordance with thedisclosed embodiments;

FIG. 4 is a flowchart that depicts a current process for determininginflow control device parameters along a horizontal well in accordancewith the disclosed embodiments;

FIG. 5 is a flowchart that depicts an algorithmic process fordetermining inflow control device parameters along a horizontal well inaccordance with the disclosed embodiments;

FIG. 6 depicts a sketch showing a wellbore and aquifer in the verticalplane of wellbore in accordance with the disclosed embodiments;

FIG. 7 is a flowchart that depicts an inflow control device optimizationalgorithm in accordance with the disclosed embodiments;

FIG. 8 is a graph that illustrates an example of a calculated velocityprofile in a wellbore in accordance with the disclosed embodiments;

FIG. 9 is a graph that illustrates an example a calculated. ICDdistribution function along a wellbore in accordance with the disclosedembodiments;

FIG. 10 is a graph that illustrates an example a variation of the ICDhole diameter corresponding to the ICD distribution function of FIG. 9in accordance with the disclosed embodiments; and

FIG. 11 is a block diagram illustrating one embodiment of a system forimplementing the disclosed embodiments.

DETAILED DESCRIPTION

The disclosed embodiments include a system and method for improvingproduction of an oil well by optimizing inflow control device parametersalong a horizontal wellbore. The disclosed embodiments and advantagesthereof are best understood by referring to FIGS. 1-11 of the drawings,like numerals being used for like and corresponding parts of the variousdrawings. Other features and advantages of the disclosed embodimentswill be or will become apparent to one of ordinary skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional features and advantages be includedwithin the scope of the disclosed embodiments. Further, the illustratedfigures are only exemplary and are not intended to assert or imply anylimitation with regard to the environment, architecture, design, orprocess in which different embodiments may be implemented.

As stated above, the use of inflow control devices can effectively delaythe water/gas breakthrough while increasing oil recovery as aconsequence. As an example, FIG. 3 depicts a graph that compares oilproduction versus water breakthrough for a horizontal well that usesinflow control devices and a horizontal well that does not use inflowcontrol devices in accordance with the disclosed embodiments. In thedepicted example, the dotted plots 310 and 320 respectively depict theoil production and water breakthrough of a horizontal well that does notuse inflow control devices. As can be seen from the graph, the dottedplot 320 rises quickly and thus causing oil production (dotted plot 310)to decrease rapidly. In contrast, oil production plot 330 and waterbreakthrough plot 340 respectively indicate oil production and waterbreakthrough of a horizontal well that uses inflow control devices tocreate a balanced inflow along the horizontal section. As shown, the useof inflow control devices causes an increase in oil production bydelaying the water breakthrough. Although FIG. 3 illustrates wellproduction versus water breakthrough, similar results are achieved bydelaying gas breakthrough as well.

Now that the benefits of ICDs have been shown, the disclosed embodimentsaddresses the issue of how to best place and/or configure the ICDs forachieving optimal production from a horizontal well. To begin with, acurrent process 400 for determining inflow control device parametersalong a horizontal well is depicted in FIG. 4. In the process 400, amodel of the wellbore is built in a wellbore simulator at step 410. Anexample of a wellbore simulator is NETool™ Simulation Software availablefrom Landmark Graphics Corporation. During this step, certain well andreservoir parameters such as, but not limited to, water cut,permeability, and skin models are configured in the wellbore simulatorsoftware. At step 420, a user configures/modifies the ICD parameters inthe wellbore simulator software. For example, in one embodiment, theuser may manually configure the number of ICDs for a wellbore, theplacement of the various ICDs along the wellbore, and the types of ICDsutilize. For example, the user may begin by configuring a uniformdistribution of ICDs of the same design along the wellbore. At step 430,the user initiates the simulation based on the entered ICD parameters.The user then analyzes the inflow profile at step 440 and determineswhether the results are satisfactory at step 450. If the results are notsatisfactory to the user, the user can repeat the process by modifyingone or more of the ICD parameters at step 420. If the results aresatisfactory, in one embodiment, the results can be outputted at step460A and used as guidance for optimal ICD placement in the field. Inanother embodiment, as shown in step 460B, the completed model may beexported into a reservoir simulator tool such as, but not limited to,Nexus® reservoir simulation software also available from LandmarkGraphics Corporation, for performing time-dependent simulation.

In contrast to the current process 400, FIG. 5 illustrates a flowchartthat depicts an algorithmic process 500 for determining ICD parametersalong a horizontal well for optimizing production in accordance with thedisclosed embodiments. Process 500 begins by building a model of awellbore in a wellbore simulator at step 510. Similar to the currentprocess, during this step, certain well and reservoir parameters suchas, but not limited to, water cut, permeability, and skin models areconfigured in the wellbore simulator software. However, instead of thecurrent manual trial and error process, the process 500 executes an ICDoptimization algorithm at step 520 to determine the optimal ICDparameters. As described above, these ICD parameters may include, butare not limited to, the number of ICDs for a wellbore, the placement ofthe various ICDs along the wellbore, and the types of ICDs beingutilized. In one embodiment, the types of ICDs may cause varyingpressure drops due to different hole densities, hole diameters, holetypes, hole distance, number of holes, etc. Once the optimal ICDparameters are determined, in one embodiment, they can be outputted atstep 530A and directly used for practical completion design.Alternatively, or in addition to, in some embodiments, the results maybe exported as a part of the completion model for input into a reservoirsimulator tool for performing time-dependent simulation as indicated atstep 530B.

In order to help illustrate one approach to developing an ICDoptimization algorithm, FIG. 6 depicts a sketch showing a wellbore andaquifer in the vertical plane of wellbore. In one embodiment, the ICDoptimization algorithm is implemented using a simplified model ofaquifer water motion near a wellbore. Typical horizontal dimensions ofthe wellbore (L) are of order of kilometers, while the typical distancebetween the wellbore and the aquifer (Lr) usually don't exceed severaldozen meters. Under these conditions, in one embodiment, the horizontaltransport of oil and water can be neglected and the pressure fieldaround the wellbore is logarithmic such that in the vertical plane ofwellbore, as shown in FIG. 6, the water transport to the wellbore may bedescribed by the following equations:

$\begin{matrix}{u_{y} = {\frac{k_{w}}{\mu_{w}}\left\{ {\frac{\left\lbrack {p^{B} - {p^{e}(z)}} \right\rbrack}{{\ln\left( \frac{r_{B}}{r_{0}} \right)}\left\lbrack {{y_{w}(z)} - y} \right\rbrack} - {\left( {\rho_{w} - \rho_{o}} \right)g}} \right\}}} & \left( {{Equation}\mspace{14mu} 1} \right) \\{v_{y} = {\frac{\partial y}{\partial t} = {\frac{1}{\gamma}u_{y}}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$whereρ_(o) is the density of oil,μ_(w), ρ_(w), and k_(w) are the viscosity, density and formationpermeability for water,y_(w) is the vertical velocity of water,y is the vertical coordinate,g is the gravity acceleration,γ is the formation porosity,v_(y) is the speed of the rising water front in the plane of thewellbore,p^(B) and p^(e) are the pressure values at the reservoir boundary andnext to the wellbore surface, andr_(B) and r_(o) are the radial coordinates of the reservoir boundary andthe wellbore surface.

The last term in the brackets in Equation 1 accounts for water movementin the vertical pressure gradient created by the oil-bearing layer offormation. In one embodiment, Equation 1 can be integrated to yield thetime required for water level to reach the wellbore:

$\begin{matrix}{{t = {\frac{1}{A}\left\lbrack {{B\mspace{11mu}{\ln\left( \frac{B}{B - {H(z)}} \right)}} - {H(z)}} \right\rbrack}}{Where}} & \left( {{Equation}\mspace{14mu} 3} \right) \\{{B = \frac{P^{B} - {P^{e}(z)}}{\left( {\rho_{w} - \rho_{o}} \right)g_{y}{\ln\left( \frac{r_{B}}{r_{0}} \right)}}};} & \left( {{Equation}\mspace{14mu} 4} \right) \\{A = \frac{\gamma\;{k_{w}(z)}\left( {\rho_{w} - \rho_{o}} \right)g}{\mu_{w}}} & \left( {{Equation}\mspace{14mu} 5} \right) \\{{H(z)} = {{y_{w}(z)} - {y_{a}(z)}}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$where H is the wellbore-aquifer vertical distance.

The flow of oil in the wellbore is described by the following equations:

$\begin{matrix}{{{\frac{dV}{dz} = \frac{j}{s}};}{j = {\frac{2\pi\; k_{o}}{\mu_{o}}\frac{p^{B} - {p^{e}(s)}}{\ln\left( \frac{r_{B}}{r_{0}} \right)}}}} & \left( {{Equation}\mspace{14mu} 7} \right) \\{\frac{dp}{dz} = {{{- \frac{f_{d}}{2D}}\rho_{o}{V}V} - \frac{2\rho_{o}{Vj}}{S} - {\rho_{o}{gy}^{\prime}}}} & \left( {{Equation}\mspace{14mu} 8} \right) \\{j^{2} = {\frac{f(z)}{K}\left\lbrack {{p^{e}(z)} - {p^{i}(z)}} \right\rbrack}} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$where z is the horizontal coordinate,V and p′ are the average flow velocity and pressure,S and D are the wellbore cross-section area and diameter,j is the volumetric influx of oil per unit length of wellbore,μ_(o), ρ_(o), and k_(o) are the viscosity, density and formationpermeability for oil, andf_(d) is the Darcy friction coefficient.

Equation 7 is the continuity equation. Equation 8 is the momentumbalance equation. Equation 9 describes the dependence of the influx ofoil on the pressure difference between the flow in wellbore and theformation.

In one embodiment, the function ƒ(z) can be assumed equal to unity forsome standard placement of ICDs, characterized by the flow resistancecoefficient K. In the simplest case, when ICDs include holes withdiameters D_(or), situated at distances L_(or) from each other, thecoefficient K equals to:

$\begin{matrix}{{K = \frac{8p_{o}{L_{or}^{2}(0)}}{\pi^{2}{D_{or}^{4}(0)}}}{and}} & \left( {{Equation}\mspace{14mu} 10} \right) \\{{f(z)} = \frac{{L_{or}^{2}(z)}{D_{or}^{2}(0)}}{{L_{or}^{2}(0)}{D_{or}^{2}(z)}}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

The longitudinal variation of hole diameter or hole spacing can beaccounted for in the model by using a non-constant function ƒ(z), whichis referenced herein as the ICD distribution function. Thus, increasingthe value of f(z), based on the above equations, would result in apressure drop across the ICD wall and an increase in influx of reservoirfluids. However if the pressure difference between the reservoir and thewellbore is kept constant, the water breakthrough time (t), according toEquation 3, will decrease. Thus, by varying the ICD efficiency functionƒ(z), the disclosed embodiments are able to control the breakthroughtime of water (t).

Therefore, a desire of the disclosed embodiments is to determine anoptimal value for the ICD efficiency function ƒ(z) such that the waterbreakthrough time is the same for all points of the wellbore, asillustrated in FIG. 2, thereby reducing a possibility of waterbreakthrough. The value of ƒ(z) indicates the amount of oil that can gothrough an orifice for a certain pressure drop between the interior ofthe wellbore and the reservoir at a certain point (z) along thewellbore.

One embodiment for determining an optimal value for the ICD efficiencyfunction ƒ(z) is presented in FIG. 7, which depicts an ICD optimizationalgorithm 700 in accordance with the disclosed embodiments. The ICDoptimization algorithm 700 begins at step 710 by postulating the valueof pressure at the end of the wellbore (p^(i)). At step 720, the processassumes uniform ICD distribution everywhere along the wellbore (e.g., itsets ƒ(z)=1). The process then calculates velocity and pressuredistribution in the wellbore at step 730. For instance, in oneembodiment, the process calculates profiles of pressure inside thewellbore (p^(I)), pressure at the boundary of the reservoir (p^(B)), andvelocity (e.g., the flow density across the wall and flow of oil throughthese ICDs).

At step 740, the process calculates distribution of the breakthroughtime along the wellbore length as indicated above in equation 3. Theprocess, at step 750, determines a point along the wellbore (z₀) thathas the maximum breakthrough time (t_(max)) (i.e., t(z₀) equals(t_(max))) and sets the ICD distribution function at that location ƒ(z₀)to 1. In the following iterations, the value of ƒ(z₀) does not change,which implies that the ICD properties such as the hole diameter andspacing at this one particular location are fixed.

At the (n+1)th iteration of the process, at step 760, using Equations 3through 6, the process determines the distribution of pressure outsidethe wellbore (p^(e) _(n+1)(z)), which would yield the uniform approachtime t(z)=t_(max). At step 770, using the solution equations 7 through9, obtained at step 730, the process determines the corresponding ICDdistribution function value at this iteration: ƒ_(n+1)(z)=j_(n)²k[p_(n+1) ^(e)(z)−p_(n) ^(i)(z)]⁻¹.

At step 780, the process determines whether the flow distributionsufficiently convergences |ƒ_(n+1)(z)−ƒ_(n)(z)|<ϵ. ϵ is a value thatindicates good convergence of the algorithm. For example, in oneembodiment, based on numerical tests, a value of ϵ=10⁻⁶ may be used asindicative of good convergence of the algorithm. If the processdetermines at step 780 that the flow distribution does not sufficientlyconverge, the process performs another iteration of the algorithm byreturning to step 730, but instead of assuming even flow everywhere asinitially set in step 720, the subsequent iteration utilizes the latestdetermined ƒ(z) flow distribution from the previous iteration of thealgorithm as ƒ(z) will no longer be 1 (i.e., even distribution) as thevalue of p^(e) (i.e., pressure outside of the wellbore) has changed. Inone embodiment, the process may repeat several iterations of thealgorithm before the flow distribution sufficiently convergences at step780. However, in certain embodiments, the algorithm converges quickly(e.g., within five iterations). Once the process determines that the ICDdistribution function f(z) sufficiently converges, the processdetermines the ICD parameters (e.g., hole density/diameter, type ofholes, number of holes, and hole spacing/distance) that would yield thisdistribution using Equation 11.

Accordingly, the disclosed embodiments include a system and method thatis configured to determine the optimal ICD parameters utilizing analgorithmic process as opposed to a manual trial and error process.

Additionally, in some embodiments, the disclosed ICD optimizationalgorithm may be applied to a numerical model developed based on afinite difference solution to the above equations. The model accountsfor variable wellbore-aquifer distance, and water, oil and formationproperties. Vertical-horizontal anisotropy of permeability can beaccounted by using effective permeability. For instance, to illustratethe suggested algorithm and numerical model, in one embodiment, consideran example of a horizontal well having a diameter 0.15 m, a length 2500m, and is situated 3 m above a flat aquifer. The viscosities of oil andwater are set to 10⁻² and 10⁻³ Pas, respectively, while the permeabilityfor both liquids were set to be 0.5 Darcy. Based on the aboveconditions, numerical trials using the described numerical model anddisclosed ICD optimization algorithm demonstrated excellent convergenceand required only several runs to achieve a desired accuracy of theresults. For example, FIG. 8 illustrates the velocity profile inside thewellbore, with z coordinate starting at the toe of the wellbore.

The calculated ICD distribution function ƒ(z) resulting from theapplication of the disclosed ICD optimization algorithm is illustratedin FIG. 9. According to Equations 7 through 11, the results illustratedin FIG. 9 can be realized, for example, by varying hole-to-hole distanceL_(or) or by changing the diameter of the holes D_(or) when the distanceL_(or) is fixed. For example, if the distance L_(or) is fixed to 12 m,the variation of the ICD distribution function shown in FIG. 9 can beachieved by varying the hole diameter as shown in FIG. 10. In otherembodiments, the change of the ICD distribution function can be achievedby varying both hole diameter, ICD distance L_(or), as well as byplacement of ICDs of various designs in different parts of the well.

Referring now to FIG. 11, a block diagram illustrating one embodiment ofa system 1100 for implementing the features and functions of thedisclosed embodiments is presented. The system 1100 may be any type ofcomputing device including, but not limited to, a desktop computer, alaptop, a server, a tablet, and a mobile device. The system 1100includes, among other components, a processor 1100, main memory 1102,secondary storage unit 1104, an input/output interface module 1106, anda communication interface module 1108.

The processor 1100 may be any type or any number of single core ormulti-core processors capable of executing instructions for performingthe features and functions of the disclosed embodiments. Theinput/output interface module 1106 enables the system 1100 to receiveuser input (e.g., from a keyboard and mouse) and output information toone or more devices such as, but not limited to, printers, external datastorage devices, and audio speakers. The system 1100 may optionallyinclude a separate display module 1110 to enable information to bedisplayed on an integrated or external display device. For instance, thedisplay module 1110 may include instructions or hardware (e.g., agraphics card or chip) for providing enhanced graphics, touchscreen,and/or multi-touch functionalities associated with one or more displaydevices.

Main memory 1102 is volatile memory that stores currently executinginstructions/data or instructions/data that are prefetched forexecution. The secondary storage unit 1104 is non-volatile memory forstoring persistent data. The secondary storage unit 1104 may be orinclude any type of data storage component such as a hard drive, a flashdrive, or a memory card. In one embodiment, the secondary storage unit1104 stores the computer executable code/instructions and other relevantdata for enabling a user to perform the features and functions of thedisclosed embodiments.

For example, in accordance with the disclosed embodiments, the secondarystorage unit 1104 may permanently store the executable code/instructionsof the above-described ICD optimization algorithm 1120. The instructionsassociated with the ICD optimization algorithm 1120 are then loaded fromthe secondary storage unit 1104 to main memory 1102 during execution bythe processor 1100 for performing the disclosed embodiments. Inaddition, the secondary storage unit 1104 may store other executablecode/instructions and data 1122 such as, but not limited to, a wellboresimulator application and/or a reservoir simulation application for usewith the disclosed embodiments.

The communication interface module 1108 enables the system 1100 tocommunicate with the communications network 1130. For example, thenetwork interface module 1108 may include a network interface cardand/or a wireless transceiver for enabling the system 1100 to send andreceive data through the communications network 1130 and/or directlywith other devices.

The communications network 1130 may be any type of network including acombination of one or more of the following networks: a wide areanetwork, a local area network, one or more private networks, theInternet, a telephone network such as the public switched telephonenetwork (PSTN), one or more cellular networks, and wireless datanetworks. The communications network 1130 may include a plurality ofnetwork nodes (not depicted) such as routers, network accesspoints/gateways, switches, DNS servers, proxy servers, and other networknodes for assisting in routing of data/communications between devices.

For example, in one embodiment, the system 1100 may interact with one ormore servers 1134 or databases 1132 for performing the features of thedisclosed embodiments. For instance, the system 1100 may query thedatabase 1132 for well log information for creating a wellbore model inaccordance with the disclosed embodiments. Further, in certainembodiments, the system 1100 may act as a server system for one or moreclient devices or a peer system for peer to peer communications orparallel processing with one or more devices/computing systems (e.g.,clusters, grids).

Thus, the disclosed embodiments provide a method for determining theoptimal ICD parameters for a given wellbore utilizing an efficientalgorithmic process. For example, in certain embodiments, determiningthe optimal ICD parameters may include determining the placement of theICDs along the wellbore, the diameters of the ICDs, and/or the types ofICDs. The disclosed embodiments may be applied to coupledwellbore-reservoir simulations of various complexity levels.

In addition, in certain embodiments, a simple numerical modelimplementing the embodiments of the disclosed algorithm can be used forcalculating a starting condition for higher level coupledwellbore-reservoir models for optimization of the ICD parameters. Thesuggested numerical model can provide a very good initial guess forCPU-expensive simulations involving detailed 3D models. On another hand,it is elaborate enough to account for many physical phenomena, andreservoir conditions, varying along the wellbore. It can be easilyexpanded to include the thermal effects or the formationvertical-horizontal anisotropy by introducing the effectivepermeability.

Additionally, the disclosed ICD optimization algorithm can be used notonly for optimizing ICD parameters for preventing wellbore flooding nearaquifers, but also to optimize the ICDs in respect to gas flooding fromthe layer above the wellbore. For instance, in one embodiment, theswitch from the aquifer to the gas mode in the algorithm is performed byreplacing the water physical parameters with those of gas, withexception of the water density, which is replaced by the densitydifference: ρ_(w)−ρ_(o)->ρ_(o)−ρ_(gas). All other elements of thealgorithm would remain the same.

While specific details about the above embodiments have been described,the above hardware and software descriptions are intended merely asexample embodiments and are not intended to limit the structure orimplementation of the disclosed embodiments. For instance, although manyother internal components of the system 1100 are not shown, those ofordinary skill in the art will appreciate that such components and theirinterconnection are well known.

In addition, certain aspects of the disclosed embodiments, as outlinedabove, may be embodied in software that is executed using one or moreprocessing units/components.

Program aspects of the technology may be thought of as “products” or“articles of manufacture” typically in the form of executable codeand/or associated data that is carried on or embodied in a type ofmachine readable medium. Tangible non-transitory “storage” type mediainclude any or all of the memory or other storage for the computers,processors or the like, or associated modules thereof, such as varioussemiconductor memories, tape drives, disk drives, optical or magneticdisks, and the like, which may provide storage at any time for thesoftware programming.

Additionally, the flowchart and block diagrams in the figures illustratethe architecture, functionality, and operation of possibleimplementations of systems, methods and computer program productsaccording to various embodiments of the present invention. It shouldalso be noted that, in some alternative implementations, the functionsnoted in the block may occur out of the order noted in the figures. Forexample, two blocks shown in succession may, in fact, be executedsubstantially concurrently, or the blocks may sometimes be executed inthe reverse order, depending upon the functionality involved. It willalso be noted that each block of the block diagrams and/or flowchartillustration, and combinations of blocks in the block diagrams and/orflowchart illustration, can be implemented by special purposehardware-based systems that perform the specified functions or acts, orcombinations of special purpose hardware and computer instructions.

In summary, the disclosed embodiments include a method, apparatus, andcomputer program product for improving production of an oil well byoptimizing inflow control device parameters along a horizontal wellbore.In addition to the embodiments described above, many examples ofspecific combinations are within the scope of the disclosure, some ofwhich are detailed below.

Example 1

A computer implemented method for improving production of an oil well,the method comprising: generating a model of a wellbore in a wellboresimulator; and executing an algorithm that determines optimal parametersof inflow control devices (ICD) along a horizontal portion of thewellbore, wherein the determined optimal parameters of the inflowcontrol devices yields a substantially uniform approach of at least oneof water and gas along the horizontal portion of the wellbore.

In certain embodiments, the embodiment of Example 1 may be modified toinclude exporting the model into reservoir simulator for time-dependentsimulation. In another embodiment of Example 1, the method includesinitializing a fixed pressure value at a toe end of the wellbore andexecuting a loop of instructions until a flow distribution sufficientlyconverges. In some embodiments, the loop initially begins with an evendistribution along the horizontal portion of the wellbore and uses theflow distribution results from a prior loop for a subsequent loop.Example 1 may further include instructions for determining a point alongthe horizontal portion of the wellbore that has a maximum approach time.Still, in some embodiments of Example 1, the computer implemented methodincludes instructions for determining a pressure distribution along thehorizontal portion of the wellbore that yields a uniform breakthroughtime.

The determined optimal parameters of the inflow control devices inExample 1 may vary a diameter of holes of the inflow control devicesalong the horizontal portion of the wellbore and/or a distance betweenthe inflow control devices along the horizontal portion of the wellbore.Additionally, embodiments of the computer implemented method of Example1 as described above may be applied to a numerical model.

Example 2

A system, comprising: at least one processor; and at least one memorycoupled to the at least one processor and storing computer executableinstructions for improving production of an oil well, the computerexecutable instructions comprises instructions for: generating a modelof a wellbore in a wellbore simulator; and executing an algorithm thatdetermines optimal parameters of inflow control devices (ICD) along ahorizontal portion of the wellbore, wherein the determined optimalparameters of the inflow control devices yields a substantially uniformapproach of at least one of water and gas along the horizontal portionof the wellbore.

Example 2.1

The system of Example 2, wherein the algorithm includes one or more ofthe following instruction: 1) instructions for initializing a fixedpressure value at a toe end of the wellbore; 2) instructions forexecuting a loop of instructions until a flow distribution sufficientlyconverges, wherein the loop initially begins with an even distributionalong the horizontal portion of the wellbore and uses the flowdistribution results from a prior loop for a subsequent loop; 3)instructions for determining a point along the horizontal portion of thewellbore that has a maximum approach time; and 4) instructions fordetermining a pressure distribution along the horizontal portion of thewellbore that yields a uniform approach time.

Example 3

A non-transitory computer readable medium comprising computer executableinstructions for improving well production, the computer executableinstructions when executed causes one or more machines to performoperations comprising: generating a model of a wellbore in a wellboresimulator; and executing an algorithm that determines optimal parametersof inflow control devices (ICD) along a horizontal portion of thewellbore, wherein the determined optimal parameters of the inflowcontrol devices yields a substantially uniform approach of at least oneof water and gas along the horizontal portion of the wellbore.

Example 3.1

The non-transitory computer readable medium of Example 3, wherein thealgorithm includes instructions for executing a loop of instructionsuntil a flow distribution sufficiently converges, wherein the loopinitially begins with an even distribution along the horizontal portionof the wellbore and uses the flow distribution results from a prior loopfor a subsequent loop, and wherein the loop includes instructions fordetermining a point along the horizontal portion of the wellbore thathas a maximum approach time; determining a pressure distribution alongthe horizontal portion of the wellbore that yields a uniform approachtime; determining the flow distribution corresponding to the determinedpressure distribution; and determining whether the flow distributionsufficiently converges.

The above specific example embodiments are not intended to limit thescope of the claims. The example embodiments may be modified byincluding, excluding, or combining one or more features or functionsdescribed in the disclosure.

In addition, as used herein, the singular forms “a”, “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. It will be further understood that the terms“comprise” and/or “comprising,” when used in this specification and/orthe claims, specify the presence of stated features, integers, steps,operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, integers, steps,operations, elements, components, and/or groups thereof. Thecorresponding structures, materials, acts, and equivalents of all meansor step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described to explain the principles of theinvention and the practical application, and to enable others ofordinary skill in the art to understand the invention for variousembodiments with various modifications as are suited to the particularuse contemplated. The scope of the claims is intended to broadly coverthe disclosed embodiments and any such modification.

The invention claimed is:
 1. A system, comprising: at least one processor; and a memory coupled to the at least one processor and storing processor-executable instructions, which, when executed by the at least one processor, cause the at least one processor to perform a plurality of functions, including functions to: generate a wellbore model representing an actual wellbore within a reservoir formation; initialize an inflow control device (ICD) distribution function associated with the generated wellbore model according to a uniform ICD distribution, the ICD distribution function representing inflow control devices at different points along a portion of the generated wellbore model corresponding to a horizontal portion of the actual wellbore; simulate a flow of reservoir fluid from the reservoir formation into the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore via the inflow control devices represented by the ICD distribution function, wherein the simulation of the flow of the reservoir fluid is performed over a plurality of iterations until it is determined that a distribution of the simulated flow of the reservoir fluid yields a uniform approach time for the reservoir fluid across all of the different points along the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore, and wherein the functions performed by the at least one processor at each iteration of the plurality of iterations include functions to: determine a pressure distribution in the generated wellbore model; determine a point along the portion of the generated wellbore model where the simulated flow of the reservoir fluid has a maximum approach time; based on the pressure distribution; modify the ICD distribution function based on the determined point; and determine whether the distribution of the simulated flow of the reservoir fluid according to the modified ICD distribution function falls within a predetermined convergence value indicating that the simulated flow of the reservoir fluid yields the uniform approach time for the reservoir fluid across all of the different points along the portion of the generated wellbore model; and determine one or more optimal parameters for actual inflow control devices along the horizontal portion of the actual wellbore to yield the uniform approach time of the reservoir fluid during a production operation within the reservoir formation, based on the ICD distribution function as modified during the plurality of iterations of the simulation, wherein the one or more optimal parameters are used to configure the actual inflow control devices to control an actual flow of reservoir fluid from the reservoir formation into the actual wellbore during the production operation.
 2. The system of claim 1, wherein the functions performed by the at least one processor further comprise functions to export the generated wellbore model into a reservoir simulator for time-dependent simulation.
 3. The system of claim 1, wherein the functions performed by the at least one processor further comprise functions to initialize a pressure value at a point in the generated wellbore model corresponding to a toe end of the actual wellbore.
 4. The system of claim 1, wherein the functions performed by the at least one processor further comprise functions to adjust one or more parameters of the inflow control devices as represented in the generated wellbore model over the plurality of iterations of the simulation until a distribution of the reservoir fluid along the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore sufficiently converges during the plurality of iterations of the simulation.
 5. The system of claim 1, wherein the functions performed by the at least one processor further comprise functions to determine which of the different points along the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore has the maximum approach time.
 6. The system of claim 1, wherein the functions performed by the at least one processor further comprise functions to determine a pressure distribution along the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore that yields the uniform approach time.
 7. The system of claim 1, wherein the determined one or more optimal parameters vary a diameter of holes of the actual inflow control devices and a distance between the actual inflow control devices along the horizontal portion of the actual wellbore.
 8. The system of claim 4, wherein the distribution of the simulated flow of the reservoir fluid along the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore sufficiently converges within five iterations.
 9. A non-transitory computer readable medium comprising computer executable instructions, which, when executed by a computer causes the computer to perform a plurality of functions, including functions to: generate a wellbore model representing an actual wellbore within a reservoir formation; initialize an inflow control device (ICD) distribution function associated with the generated wellbore model according to a uniform ICD distribution, the ICD distribution function representing inflow control devices at different points along a portion of the generated wellbore model corresponding to a horizontal portion of the actual wellbore; simulate a flow of reservoir fluid from the reservoir formation into the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore via the inflow control devices represented by the ICD distribution function, wherein the simulation of the flow of the reservoir fluid is performed over a plurality of iterations until it is determined that a distribution of the simulated flow of the reservoir fluid yields a uniform approach time for the reservoir fluid across all of the different points along the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore, and wherein the functions performed by the at least one processor at each iteration of the plurality of iterations include functions to: determine a pressure distribution in the generated wellbore model; determine a point along the portion of the generated wellbore model where the simulated flow of the reservoir fluid has a maximum approach time, based on the pressure distribution; modify the ICD distribution function based on the determined point; and determine whether the distribution of the simulated flow of the reservoir fluid according to the modified ICD distribution function falls within a predetermined convergence value indicating that the simulated flow of the reservoir fluid yields the uniform approach time for the reservoir fluid across all of the different points along the portion of the generated wellbore model; and determine one or more optimal parameters for actual inflow control devices along horizontal portion of the wellbore to yield the uniform approach time of the reservoir fluid during a production operation within the reservoir formation, based on the ICD distribution function as modified during the plurality of iterations of the simulation, wherein the one or more optimal parameters are used to configure the actual inflow control devices to control an actual flow of reservoir fluid from the reservoir formation into the actual wellbore during the production operation.
 10. The non-transitory computer readable medium of claim 9, wherein the functions performed by the computer further comprise functions to: determine a pressure distribution that yields the uniform approach time of the simulated reservoir fluid flow along the portion of the generated wellbore model corresponding to the horizontal portion of the actual wellbore, and determine an ICD distribution along the horizontal portion of the actual wellbore corresponding to the determined pressure distribution along the portion of the generated wellbore model. 